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frolloos
Topic Author
Posts: 1581
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### volatility

Setting: Black-Scholes with deterministic volatility.

Vanilla options are priced with volatility equal to remaining variance/volatility $\int_t^T \sigma^2(u) du$.

What kind of option, that is delta-hedgeable, has as input at current time $t$ not the remaining variance, but the total variance $\int_0^T \sigma^2(u) du$ from $u=0$ to $u = T$?

Is it a timer option that I should be looking at?

Alan
Posts: 9867
Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: volatility

Ignoring the delta-hedgeable requirement, my thought was a capped variance swap, as the cap is triggered by the total variance.
Last edited by Alan on December 2nd, 2019, 4:40 pm, edited 1 time in total.

frolloos
Topic Author
Posts: 1581
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: volatility

Thanks - yes maybe that could work. Preferably I could somehow relate the instrument, whatever it is, to a single vanilla option (by eg choosing an appropriate strike), but I am starting to believe that may be impossible.

frolloos
Topic Author
Posts: 1581
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: volatility

The attachment, which is a very rough draft, hopefully clarifies what I am trying to do.

I can incorporate total volatility, but using a strip of options which is not delta-hedgeable as it involves an untradable "auxiliary" process. Hence, my search for something simpler, if it exists.[attachment=0]taylormade2.pdf[/attachment
Attachments